On the Complexity of Query Result Diversification

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1

Improving package recommendations through query relaxation

Recommendation systems aim to identify items that are likely to be of interest to users. In many cases, users are interested in package recommendations as collections of items. For example, a dietitian may wish to derive a dietary plan as a collection of recipes that is nutritionally balanced, and a travel agent may want to produce a vacation package as a coordinated collection of travel and hotel reservations. Recent work has explored extending recommendation systems to support packages of items. These systems need to solve complex combinatorial problems, enforcing various properties and constraints defined on sets of items. Introducing constraints on packages makes recommendation queries harder to evaluate, but also harder to express: Queries that are under-specified produce too many answers, whereas queries that are over-specified frequently miss interesting solutions. In this paper, we study query relaxation techniques that target package recommendation systems. Our work offers three key insights: First, even when the original query result is not empty, relaxing constraints can produce preferable solutions. Second, a solution due to relaxation can only be preferred if it improves some property specified by the query. Third, relaxation should not treat all constraints as equals: some constraints are more important to the users than others. Our contributions are threefold: (a) we define the problem of deriving package recommendations through query relaxation, (b) we design and experimentally evaluate heuristics that relax query constraints to derive interesting packages, and (c) we present a crowd study that evaluates the sensitivity of real users to different kinds of constraints and demonstrates that query relaxation is a powerful tool in diversifying package recommendations

A Harmonic Extension Approach for Collaborative Ranking

We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank approximation methods using convex optimization and the nuclear norm, we formulate matrix completion as a series of semi-supervised learning problems, and propagate the known ratings to the missing ones on the user-user or item-item graph globally. The semi-supervised learning problems are expressed as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and can be discretized by a point integral method. We show that our approach does not impose a low-rank Euclidean subspace on the data points, but instead minimizes the dimension of the underlying manifold. Our method, named LDM (low dimensional manifold), turns out to be particularly effective in generating rankings of items, showing decent computational efficiency and robust ranking quality compared to state-of-the-art methods

Reflections on the EU objectives in addressing aggressive tax planning and harmful tax practices Final Report. CEPS Report November 2019

This Report analyses the EU’s instruments to tackle aggressive tax planning and harmful tax practices. Based on desk research, interviews with stakeholders and expert assessments, it considers the coherence, relevance, and added value of the EU’s approach. The instruments under analysis are found to be internally coherent and consistent with other EU policies and with the international tax agenda, in particular with the OECD/G20 BEPS framework. The Report also confirms the continued relevance of most of the original needs and problems addressed by the EU’s initiatives in the field of tax avoidance. There is also EU added value in having common EU instruments in the field to bolster coordination and harmonise the implementation of tax measures. One cross-cutting issue identified is the impact of digitalisation on corporate taxation. Against this background, the Report outlines potential improvements to the EU tax strategy such as: making EU tax systems fit for the digital era; leading the international debate on tax avoidance; enabling capacity building in Member States and developing countries; strengthening tax good governance in third countries; ensuring a consistent approach at home and abroad; achieving a level playing field for all companies; and increasing tax certainty and legal certainty